I am a mathematica novice so I don't even know if the
following is a stupid question.
I have the expression shown below :
duck = 1/2(B1*a^2 + B2*ac + B3*c^2 + B4*a + B5*c + B6)
where
B1 = 10 - 6*cos(x) + 3*cos(3x) - 10*cos(4x) + 3*cos(5x)
B2 = 6 - 6*cos(3x) - 6*cos(4x) + 6*cos(5x)
B3= 14 - 5*cos(x) - 2*cos(2x) - 14*cos(3x) + 4*cos(4x) + 3*cos(5x)
B4 = -32 + 32*cos(x) - 16*cos(3x) + 32*cos(4x) - 16*cos(5x)
B5 = -16 + 16*cos(3x) + 16*cos(4x) - 16*cos(5x)
B6 = 32 - 32*cos(x) + 16*cos(3x) - 32*cos(4x) + 16*cos(5x)
I was wondering if there was any way to ask mathematica
to find some expression, temp, which involves a and c
( for example it might be a/(a+c)) and use it
to simplify the expression, duck, so that duck
can be written in the following form called simpduck:
simpduck = f1(temp)*cos(x) + f2(temp)*cos(2x) + f3(temp)*cos(3x)
+ f4(temp)*cos(4x) +f5(temp)*cos(5x).
it is fine if f1=f2=f3=f4=f5 etc and if trigonometric identities
have to
be used so that it only goes upto say cos(3x), this is fine also.
for example, if temp=a/(a+c), then maybe f(temp)=temp^2 or whatever
?
basically, my goal is to have a and c together instead of
seperated.
thank you very much and i apologize if this is impossible to do ?
Mark